The problem is, even if there were another app store, you'd have to persuade people to go there. Amazon manages, because they're a big name, but even for setting up their store, you still have to go through the "Installing apps from somewhere else could end up with horrible evil things happening. Do you really want to accept this risk" dialog.
People will probably think "I'd bought stuff from Amazon, I know it'll be ok" but for something that - to start with especially - may have only a fairly small number of apps? Why would a new user do that? How would they even find the app store? It's a very tricky proposition, unfortunately.
I my main app, I want a way to get donations towards the cost of running the site that the app connects to; members who have donated don't get a reminder banner in the app.
I thought about using the Play Store. And then I thought about the stupid moralising of Google, and the changes to the app I'd have to do to fit their skewed view of the world. And the 30% of our donations they'd cream off. So I decided to do it differently.
I added a page to the website, with minimal formatting, that creates a form with a PayPal donate button (I wanted to avoid the library, because we have members in lots of countries, and support doesn't seem uniform). Tap the donate link, the app opens a web view, passing an identifier to the website script. That creates a form with a custom field embedded, so that the transaction can be linked to a specific user.
When a donation is made via the normal PayPal mobile web flow, the web site gets a PayPal IPN via the usual callback. That updates the user's record in the website. I then added an extra field to the data I return to the app from our API, indicating whether or not they're a recent donor, and that's used to show or hide the reminder banner.
Now, I know this isn't as slick as having a simple Google in-app payment (and perhaps consuming a donation after, say, a year), but it also means that if someone donates €10, we actually get €9.31, or for £20, we get £19.12; use in-app payments and we'd get €7 and £14 respectively.
There are lots of other ways to handle this (in some cases, the PayPal library might be a good thing to include in your app). And yes, it's not as integrated as IAP. But with a bit of thought, you can manage a fairly reasonable experience, and retain more of your cash.